Carbon cluster structures and stabilities predicted from solid-state potentials

An empirical potential-energy function comprising two- and three-body terms, whose parameters have been determined from the properties of diamond and graphite, is used to study the structures and energies of carbon microclusters. The binding energy per atom of smaller linear clusters increases monotonically with the number of atoms, whereas cyclic clusters display an optimal energy per atom for six-membered rings. The energies of fullerenes are sensitive to nuclearity and shape, with icosahedral C₆₀ and D_5h C ₇₀ being the most stable clusters. The potential predicts the binding energy of C₆₀ to be 7.25 eV per atom, in good agreement with experimental measurements. For larger clusters, spherical fragments of cubic bulk structures have been investigated; diamond fragments become relatively more stable than other cubic fragments for more than approximately 100 atoms. Open nanotubes are found to be most stable for circumferences containing five hexagons. Vibrational frequencies were calculated and correlated with experimental results for some clusters.